\documentclass[11pt]{article}

\begin{document}

\begin{theorem}
\begin{equation}
x+5=6
\end{equation}
\end{theorem}

\begin{theorem}\end{theorem}

\begin{proof}
$:)$
$$:/$$
\end{proof}

\begin{lemma}
$test$
\end{lemma}

\begin{lemma}$$formula1$$, $formula2$, ignorable text here\end{lemma}

\begin{proof}
\begin{equation}
4*4/4=y
\end{equation}
\end{proof}

\end{document}